You need to use a load cell amplifier between the Arduino and the load cell. Load cells are around 350 Ohms. Four wire. And the signal that needs to be measured are very small.
The current will not be too high. The question indicates that you don't understand the application. (and therefore you are looking for help)
Here are some useful links.
A typical load cell has an output of 2 millivolts per volt of excitation voltage at the full rated weight. For example, if 5 volts were used for the excitation voltage, and the output is 2 mV/volt, then the voltage out would be 10mV at full scale. The voltage difference (compared to the unloaded load cell) is what is measure.
If the excitation voltage (just a technical name for applied voltage) were 5 volts, the voltage at the output terminals, measured from the negative terminal, would be 2.5 volts, half of the applied voltage. But this 2.5 volts is not the measured output. What is measured is the difference between the +signal and the -signal wires.